Neurons in dissociated cell cultures stained immunohistochemically with tetanus toxin and analyzed for fractal dimension, provide an optimal system for the quantitative study of the development of two-dimensional patterns of neurite outgrowth. The cultures contain neurons that can be grouped on the basis of visually perceived structural complexity, and that the grouping is consistent with estimates of fractal dimension and with other Euclidean measures of the dendritic tree. Moreover, fractal dimension is a objective measure that can be used to monitor the morphological differentiation of each of the four groups analyzed. Curves of fractal dimension as a function of time in culture reflect differences in each of cell types. Moreover, during the first week after plating, increases in fractal dimension do not parallel increases in other measures of dendrite growth.. Dendrite growth proceeds linearly for all groups whereas fractal dimension increases exponentially and then plateaus. The dendrites continue to grow and form additional branches without further increases in complexity. Thus, during early development, fractal dimension measures a unique property whereas in later development, it may serve as an index which encompasses a number of other growth measures.